Subgroups — C₄₇×#15128 #26054826

Order 12032.

1822 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#395	C₂	1	2	yes	maximal
3	C₂×C₄₇×#389	C₂	1	2	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1446	C₂	1	2	yes	maximal
6	C₄₇×#1444	C₂	1	2	yes	maximal
7	C₄₇×#1441	C₂	1	2	yes	maximal
8	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₄₇	—	2	8	no	—
12	C₂×C₄⋊Q₈×C₄₇	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#395	—	2	8	no	—
23	C₄₇×#389	—	2	8	no	—
24	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
25	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×#95×C₄₇	C₂²	1	4	yes	—
28	C₂×#95×C₄₇	C₂²	1	4	yes	—
29	C₂×#95×C₄₇	C₂²	1	2	yes	—
30	C₂×#95×C₄₇	C₂²	1	2	yes	—
31	C₂×#95×C₄₇	C₂²	1	4	yes	—
32	C₂²×Q₈×C₄₇	—	2	8	no	—
33	C₂²×Q₈×C₄₇	—	2	4	no	—
34	C₂²×Q₈×C₄₇	—	2	4	no	—
35	C₂²×Q₈×C₄₇	—	2	4	no	—
36	C₂²×Q₈×C₄₇	—	4	4	no	—
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₄₇	—	2	32	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
59	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
60	C₂×C₄⋊C₄×C₄₇	D₄	1	8	yes	—
61	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₇	Q₈	1	8	yes	complemented
63	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	complemented
64	C₂×C₄²×C₄₇	—	2	4	no	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	—	2	4	no	—
69	C₂×C₄²×C₄₇	D₄	1	4	yes	—
70	C₂×C₄²×C₄₇	Q₈	1	4	yes	complemented
71	#95×C₄₇	—	2	2	no	—
72	#95×C₄₇	—	2	2	no	—
73	#95×C₄₇	—	2	8	no	—
74	#95×C₄₇	—	2	8	no	—
75	#95×C₄₇	—	2	4	no	—
76	#95×C₄₇	—	2	4	no	—
77	#95×C₄₇	—	4	4	no	—
78	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
79	C₂×Q₈×C₄₇	—	2	16	no	—
80	C₂×Q₈×C₄₇	—	4	16	no	—
81	C₂×Q₈×C₄₇	—	4	16	no	—
82	C₂×Q₈×C₄₇	—	4	8	no	—
83	C₂×Q₈×C₄₇	—	4	8	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	4	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	2	4	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	—
127	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
132	C₂²×C₄×C₄₇	#41	1	2	yes	—
133	C₂²×C₄×C₄₇	#41	1	2	yes	—
134	C₂²×C₄×C₄₇	#41	1	2	yes	—
135	C₄⋊C₄×C₄₇	—	2	16	no	—
136	C₄⋊C₄×C₄₇	—	2	16	no	—
137	C₄⋊C₄×C₄₇	—	2	8	no	—
138	C₄⋊C₄×C₄₇	—	2	8	no	—
139	C₄⋊C₄×C₄₇	—	2	16	no	—
140	C₄⋊C₄×C₄₇	—	4	16	no	—
141	C₄²×C₄₇	—	2	8	no	—
142	C₄²×C₄₇	—	2	8	no	—
143	C₄²×C₄₇	—	4	4	no	—
144	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
149	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
154	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
155	Q₈×C₄₇	—	4	32	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	8	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	8	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	8	no	—
178	C₂×C₄×C₄₇	—	2	8	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	8	no	—
181	C₂×C₄×C₄₇	—	2	8	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	4	no	—
185	C₂×C₄×C₄₇	—	4	4	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	4	4	no	—
189	C₂×C₄×C₄₇	—	4	1	no	—
190	C₂×C₄×C₄₇	—	4	1	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	4	no	—
193	C₂×C₄×C₄₇	—	4	4	no	—
194	C₂×C₄×C₄₇	—	4	4	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	4	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	4	no	—
199	C₂×C₄×C₄₇	#120	1	4	yes	—
200	C₂×C₄×C₄₇	#121	1	4	yes	—
201	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
202	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
203	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
204	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
205	C₂×C₄×C₄₇	C₄⋊Q₈	1	8	yes	—
206	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	complemented
207	#15128	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
213	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
216	C₂²×C₄₇	#532	1	1	yes	characteristic
217	C₂²×C₄₇	#533	1	1	yes	characteristic
218	C₂²×C₄₇	#533	1	1	yes	characteristic
219	C₂²×C₄₇	#535	1	1	yes	characteristic
220	C₂²×C₄₇	#536	1	1	yes	characteristic
221	C₂²×C₄₇	#542	1	2	yes	—
222	C₂²×C₄₇	#544	1	2	yes	—
223	C₂²×C₄₇	D₄²	1	2	yes	—
224	C₂²×C₄₇	#546	1	2	yes	—
225	C₂²×C₄₇	#548	1	2	yes	—
226	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
227	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
228	C₂²×C₄₇	#554	1	2	yes	—
229	C₂²×C₄₇	#557	1	2	yes	—
230	C₂²×C₄₇	Q₈²	1	2	yes	—
231	C₄×C₄₇	—	2	4	no	—
232	C₄×C₄₇	—	2	4	no	—
233	C₄×C₄₇	—	2	4	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	4	8	no	—
237	C₄×C₄₇	—	4	2	no	—
238	C₄×C₄₇	—	4	8	no	—
239	C₄×C₄₇	#395	1	8	yes	complemented
240	C₂²×C₄⋊Q₈	C₂×C₄₇	1	1	yes	characteristic
241	C₂×#395	C₂×C₄₇	1	2	yes	—
242	C₂×#389	C₂×C₄₇	1	2	yes	—
243	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
244	#1446	C₂×C₄₇	1	2	yes	—
245	#1444	C₂×C₄₇	1	2	yes	—
246	#1441	C₂×C₄₇	1	2	yes	—
247	C₄⋊#95	C₂×C₄₇	1	2	yes	—
248	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic
249	C₂×C₄₇	C₂×#395	1	1	yes	characteristic
250	C₂×C₄₇	#2408	1	1	yes	characteristic
251	C₂×C₄₇	#2409	1	1	yes	characteristic
252	C₂×C₄₇	#2451	1	2	yes	—
253	C₂×C₄₇	#2452	1	2	yes	—
254	C₂×C₄₇	#2546	1	1	yes	characteristic
255	C₂×C₄₇	#2550	1	2	yes	—
256	C₂×C₄₇	#2551	1	2	yes	—
257	C₂×C₄₇	#2567	1	1	yes	characteristic
258	C₂×C₄₇	#2628	1	1	yes	characteristic
259	C₂×C₄₇	#2857	1	1	yes	characteristic
260	C₂³×Q₈	C₂²×C₄₇	1	2	yes	—
261	C₂×C₄⋊Q₈	—	2	8	no	—
262	C₂×C₄⋊Q₈	—	2	4	no	—
263	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
264	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
268	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
269	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
270	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
271	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
272	#395	—	2	8	no	—
273	#389	—	2	8	no	—
274	C₄×C₄⋊C₄	—	2	4	no	—
275	C₂×#95	C₂²×C₄₇	1	4	yes	—
276	C₂×#95	C₂²×C₄₇	1	2	yes	—
277	C₂×#95	C₂²×C₄₇	1	2	yes	—
278	C₂×#95	C₂²×C₄₇	1	4	yes	—
279	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
280	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
281	C₂×#95	C₂²×C₄₇	1	4	yes	—
282	C₄₇	#15128	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₈	—	2	8	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	2	4	no	—
286	C₂²×Q₈	—	2	4	no	—
287	C₂²×Q₈	—	4	4	no	—
288	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
290	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
291	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
297	C₄⋊Q₈	—	2	32	no	—
298	C₂×C₄⋊C₄	—	2	8	no	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	—	2	8	no	—
309	C₂×C₄⋊C₄	—	2	8	no	—
310	C₂×C₄⋊C₄	—	4	4	no	—
311	C₂×C₄⋊C₄	D₄×C₄₇	1	8	yes	—
312	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
313	C₂×C₄⋊C₄	Q₈×C₄₇	1	8	yes	complemented
314	C₂×C₄⋊C₄	Q₈×C₄₇	1	4	yes	complemented
315	C₂×C₄²	—	2	4	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	4	no	—
320	C₂×C₄²	D₄×C₄₇	1	4	yes	—
321	C₂×C₄²	Q₈×C₄₇	1	4	yes	complemented
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	8	no	—
325	#95	—	2	4	no	—
326	#95	—	2	8	no	—
327	#95	—	2	4	no	—
328	#95	—	4	4	no	—
329	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
330	C₂×Q₈	—	2	16	no	—
331	C₂×Q₈	—	4	16	no	—
332	C₂×Q₈	—	4	16	no	—
333	C₂×Q₈	—	4	8	no	—
334	C₂×Q₈	—	4	8	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
368	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
375	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
376	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
377	C₂²×C₄	C₂×Q₈×C₄₇	1	8	yes	—
378	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
379	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
380	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
381	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
382	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
383	C₂²×C₄	#41×C₄₇	1	2	yes	—
384	C₂²×C₄	#41×C₄₇	1	2	yes	—
385	C₂²×C₄	#41×C₄₇	1	2	yes	—
386	C₄⋊C₄	—	2	16	no	—
387	C₄⋊C₄	—	2	16	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	2	16	no	—
391	C₄⋊C₄	—	4	16	no	—
392	C₄²	—	2	8	no	—
393	C₄²	—	2	8	no	—
394	C₄²	—	4	4	no	—
395	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
396	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
397	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
398	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
399	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
400	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
401	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
402	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
403	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
404	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
405	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
406	Q₈	—	4	32	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	#120×C₄₇	1	4	yes	—
451	C₂×C₄	#121×C₄₇	1	4	yes	—
452	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
453	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
454	C₂×C₄	C₂²⋊Q₈×C₄₇	1	8	yes	—
455	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	—
456	C₂×C₄	C₄⋊Q₈×C₄₇	1	8	yes	—
457	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	complemented
458	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
459	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
460	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
461	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
462	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
463	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
464	C₂²	C₂×C₄⋊Q₈×C₄₇	1	2	yes	—
465	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
466	C₂²	C₄₇×#532	1	1	yes	characteristic
467	C₂²	C₄₇×#533	1	1	yes	characteristic
468	C₂²	C₄₇×#533	1	1	yes	characteristic
469	C₂²	C₄₇×#535	1	1	yes	characteristic
470	C₂²	C₄₇×#536	1	1	yes	characteristic
471	C₂²	C₄₇×#542	1	2	yes	—
472	C₂²	C₄₇×#544	1	2	yes	—
473	C₂²	D₄²×C₄₇	1	2	yes	—
474	C₂²	C₄₇×#546	1	2	yes	—
475	C₂²	C₄₇×#548	1	2	yes	—
476	C₂²	D₄×Q₈×C₄₇	1	2	yes	—
477	C₂²	D₄×Q₈×C₄₇	1	2	yes	—
478	C₂²	C₄₇×#554	1	2	yes	—
479	C₂²	C₄₇×#557	1	2	yes	—
480	C₂²	Q₈²×C₄₇	1	2	yes	—
481	C₄	—	2	4	no	—
482	C₄	—	2	4	no	—
483	C₄	—	2	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	8	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	8	no	—
489	C₄	C₄₇×#395	1	8	yes	complemented
490	C₂	C₂×C₄₇×#395	1	1	yes	characteristic
491	C₂	C₄₇×#2408	1	1	yes	characteristic
492	C₂	C₄₇×#2409	1	1	yes	characteristic
493	C₂	C₄₇×#2451	1	2	yes	—
494	C₂	C₄₇×#2452	1	2	yes	—
495	C₂	C₄₇×#2546	1	1	yes	characteristic
496	C₂	C₄₇×#2550	1	2	yes	—
497	C₂	C₄₇×#2551	1	2	yes	—
498	C₂	C₄₇×#2567	1	1	yes	characteristic
499	C₂	C₄₇×#2628	1	1	yes	characteristic
500	C₂	C₄₇×#2857	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
62. C₂×C₄⋊C₄×C₄₇	Q₈	semidirect
63. C₂×C₄⋊C₄×C₄₇	Q₈	semidirect
70. C₂×C₄²×C₄₇	Q₈	semidirect
206. C₂×C₄×C₄₇	C₄⋊Q₈	semidirect
207. #15128	C₄₇	direct (N × H)
239. C₄×C₄₇	#395	semidirect
282. C₄₇	#15128	direct (N × H)
313. C₂×C₄⋊C₄	Q₈×C₄₇	semidirect
314. C₂×C₄⋊C₄	Q₈×C₄₇	semidirect
321. C₂×C₄²	Q₈×C₄₇	semidirect
457. C₂×C₄	C₄⋊Q₈×C₄₇	semidirect
489. C₄	C₄₇×#395	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄⋊Q₈×C₄₇	2
C₂×C₄₇×#395	2
C₂×C₄₇×#389	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1446	2
C₄₇×#1444	2
C₄₇×#1441	2
C₄₇×C₄⋊#95	2
#15128	47

Subgroups — C47×#15128 #26054826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15128 #26054826